Month: September 2021

Yong Li, Shoaib Kamil, Alec Jacobson, Yotam Gingold

Communicating linear algebra in written form is challenging: mathematicians must choose between writing in languages that produce well-formatted but semantically-underdefined representations such as LaTeX; or languages with well-defined semantics but notation unlike conventional math, such as C++/Eigen. In both cases, the underlying linear algebra is obfuscated by the requirements of esoteric language syntax (as in LaTeX) or awkward APIs due to language semantics (as in C++). The gap between representations results in communication challenges, including underspecified and irreproducible research results, difficulty teaching math concepts underlying complex numerical code, as well as repeated, redundant, and error-prone translations from communicated linear algebra to executable code. We introduce I❤ LA, a language with syntax designed to closely mimic conventionally-written linear algebra, while still ensuring an unambiguous, compilable interpretation. Inspired by Markdown, a language for writing naturally-structured plain text files that translate into valid HTML, I❤ LA allows users to write linear algebra in text form and compile the same source into LaTeX, C++/Eigen, Python/NumPy/SciPy, and MATLAB, with easy extension to further math programming environments. We outline the principles of our language design and highlight design decisions that balance between readability and precise semantics, and demonstrate through case studies the ability for I❤ LA to bridge the semantic gap between conventionally-written linear algebra and unambiguous interpretation in math programming environments.

I❤️LA: Compilable Markdown for Linear Algebra

Jing Li, Tiantian Liu, Ladislav Kavan, Baoquan Chen

We propose a new algorithm for updating a Cholesky factorization which speeds up Projective Dynamics simulations with topological changes. Our approach addresses an important limitation of the original Projective Dynamics, i.e., that topological changes such as cutting, fracturing, or tearing require full refactorization which compromises computation speed, especially in real-time applications. Our method progressively modifies the Cholesky factor of the system matrix in the global step instead of computing it from scratch. Only a small amount of overhead is added since most of the topological changes in typical simulations are continuous and gradual. Our method is based on the update and downdate routine in CHOLMOD, but unlike recent related work, supports dynamic sizes of the system matrix and the addition of new vertices. Our approach allows us to introduce clean cuts and perform interactive remeshing. Our experiments show that our method works particularly well in simulation scenarios involving cutting, tearing, and local remeshing operations.

Interactive Cutting and Tearing in Projective Dynamics with Progressive Cholesky Updates

Yuchen Sun*, Xingyu Ni*, Bo Zhu, Bin Wang, Baoquan Chen

We propose a novel numerical scheme to simulate interactions between a magnetic field and nonlinearly magnetized objects immersed in it. Under our nonlinear magnetization framework, the strength of magnetic forces is effectively saturated to produce stable simulations without requiring any parameter tuning. The mathematical model of our approach is based upon Langevin’s nonlinear theory of paramagnetism, which bridges microscopic structures and macroscopic equations after a statistical derivation. We devise a hybrid Eulerian-Lagrangian numerical approach to simulating this strongly nonlinear process by leveraging the discrete material points to transfer both material properties and the number density of magnetic micro-particles in the simulation domain. The magnetic equations can then be built and solved efficiently on a background Cartesian grid, followed by a finite difference method to incorporate magnetic forces. The multi-scale coupling can be processed naturally by employing the established particle-grid interpolation schemes in a conventional MLS-MPM framework. We demonstrate the efficacy of our approach with a host of simulation examples governed by magnetic-mechanical coupling effects, ranging from magnetic deformable bodies to magnetic viscous fluids with nonlinear elastic constitutive laws.

A Material Point Method for Nonlinearly Magnetized Materials

J. A. Amador Herrera, T. Hädrich, W. Pałubicki, D. T. Banuti, S. Pirk, D. L. Michels.

Due to the complex interplay of various meteorological phenomena, simulating weather is a challenging and open research problem. In this contribution, we propose a novel physics-based model that enables simulating weather at interactive rates. By considering atmosphere and pedosphere we can define the hydrologic cycle – and consequently weather – in unprecedented detail. Specifically, our model captures different warm and cold clouds, such as mammatus, hole-punch, multi-layer, and cumulonimbus clouds as well as their dynamic transitions. We also model different precipitation types, such as rain, snow, and graupel by introducing a comprehensive microphysics scheme. The Wegener-Bergeron-Findeisen process is incorporated into our Kessler-type microphysics formulation covering ice crystal growth occurring in mixed-phase clouds. Moreover, we model the water run-off from the ground surface, the infiltration into the soil, and its subsequent evaporation back to the atmosphere. We account for daily temperature changes, as well as heat transfer between pedosphere and atmosphere leading to a complex feedback loop. Our framework enables us to interactively explore various complex weather phenomena. Our results are assessed visually and validated by simulating weatherscapes for various setups covering different precipitation events and environments, by showcasing the hydrologic cycle, and by reproducing common effects such as Foehn winds. We also provide quantitative evaluations creating high-precipitation cumulonimbus clouds by prescribing atmospheric conditions based on infrared satellite observations. With our model we can generate dynamic 3D scenes of weatherscapes with high visual fidelity and even nowcast real weather conditions as simulations by streaming weather data into our framework.

Weatherscapes: Nowcasting Heat Transfer and Water Continuity

Kai Bai, Chunhao Wang, Mathieu Desbrun, Xiaopei Liu

Predicting the fine and intricate details of a turbulent flow field in both space and time from a coarse input remains a major challenge despite the availability of modern machine learning tools. In this paper, we present a simple and effective dictionary-based approach to spatio-temporal upsampling of fluid simulation. We demonstrate that our neural network approach can reproduce the visual complexity of turbulent flows from spatially and temporally coarse velocity fields even when using a generic training set. Moreover, since our method generates finer spatial and/or temporal details through embarrassingly-parallel upsampling of small local patches, it can efficiently predict high-resolution turbulence details across a variety of grid resolutions. As a consequence, our method offers a whole range of applications varying from fluid flow upsampling to fluid data compression. We demonstrate the efficiency and generalizability of our method for synthesizing turbulent flows on a series of complex examples, highlighting dramatically better results in spatio-temporal upsampling and flow data compression than existing methods as assessed by both qualitative and quantitative comparisons.

Predicting High-Resolution Turbulence Details in Space and Time

Chaoyang Lyu, Wei Li, Mathieu Desbrun, Xiaopei Liu

The intricate motions and complex vortical structures generated by the interaction between fluids and solids are visually fascinating. However, reproducing such a two-way coupling between thin objects and turbulent fluids numerically is notoriously challenging and computationally costly:
existing approaches such as cut-cell or immersed-boundary methods have
difficulty achieving physical accuracy, or even visual plausibility, of simulations involving fast-evolving flows with immersed objects of arbitrary shapes. In this paper, we propose an efficient and versatile approach for simulating two-way fluid-solid coupling within the kinetic (lattice-Boltzmann) fluid simulation framework, valid for both laminar and highly turbulent flows, and for both thick and thin objects. We introduce a novel hybrid approach to fluid-solid coupling which systematically involves a mesoscopic double-sided bounce-back scheme followed by a cut-cell velocity correction for a more robust and plausible treatment of turbulent flows near moving (thin) solids, preventing flow penetration and reducing boundary artifacts significantly. Coupled with an efficient approximation to simplify geometric computations, the whole boundary treatment method preserves the inherent massively parallel computational nature of the kinetic method. Moreover, we propose simple GPU optimizations of the core LBM algorithm which achieve an even higher computational efficiency than the state-of-the-art kinetic fluid solvers in graphics. We demonstrate the accuracy and efficacy of our two-way coupling through various challenging simulations involving a variety of rigid body solids and fluids at both high and low Reynolds numbers. Finally, comparisons to existing methods on benchmark data and real experiments further highlight the superiority of our method.

Fast and Versatile Fluid-Solid Coupling for Turbulent Flow Simulation

• Fast and Versatile Fluid-Solid Coupling for Turbulent Flow Simulation
• Predicting High-Resolution Turbulence Details in Space and Time
• Weatherscapes: Nowcasting Heat Transfer and Water Continuity
• Ships, Splashes, and Waves on a Vast Ocean
• A Material Point Method for Nonlinearly Magnetized Materials
• Interactive Cutting and Tearing in Projective Dynamics with Progressive Cholesky Updates
• I❤️LA: Compilable Markdown for Linear Algebra
• FrictionalMonolith: A Monolithic Optimization-based Approach for Granular Flow with Contact-Aware Rigid-Body Coupling
• Spiral-Spectral Fluid Simulation
• Generalized Fluid Carving With Fast Lattice-Guided Seam Computation
• PBNS: Physically Based Neural Simulation for Unsupervised Garment Pose Space Deformation

TOG:

• Locking-Proof Tetrahedra

Nghia Truong, Cem Yuksel, Chakrit Watcharopas, Joshua A. Levine, Robert M. Kirby

Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem. We introduce particle merging-and-splitting, a simple scheme for robustly handling collisions between particles that prevents inter-penetrations of separate objects without introducing numerical instabilities. This scheme merges colliding particles at the beginning of the time-step and then splits them at the end of the time-step. Thus, collisions last for the duration of a time-step, allowing neighboring particles of the colliding particles to influence each other. We show that our merging-and-splitting method is effective in robustly handling collisions and avoiding penetrations in particle-based simulations. We also show how our merging-and-splitting approach can be used for coupling different simulation systems using different and otherwise incompatible integrators. We present simulation tests involving complex solid-fluid interactions, including solid fractures generated by fluid interactions.

Particle Merging-and-Splitting

Xu Wang, Makoto Fujisawa, Masahiko Mikawa

This paper introduces a method for simulating soil-structure coupling with water, which involves a series of visual effects, including wet granular materials, seepage flows, capillary action between grains, and dam breaking simulation. We develop a seepage flow based SPH-DEM framework to handle soil and water particles interactions through a momentum exchange term. In this framework, water is seen as a seepage flow through porous media by Darcy’s law; the seepage rate and the soil permeability are manipulated according to drag coefficient and soil porosity. A water saturation-based capillary model is used to capture various soil behaviors such as sandy soil and clay soil. Furthermore, the capillary model can dynamically adjust liquid bridge forces induced by surface tension between soil particles. The adhesion model describes the attraction ability between soil surfaces and water particles to achieve various visual effects for soil and water. Lastly, this framework can capture the complicated dam-breaking scenarios caused by overtopping flow or internal seepage erosion that are challenging to simulate.

Visual Simulation of Soil-Structure Destruction with Seepage Flows

Bruno Roy, Pierre Poulin, Eric Paquette

We present a novel up-resing technique for generating high-resolution liquids based on scene flow estimation using deep neural networks. Our approach infers and synthesizes small- and large-scale details solely from
a low-resolution particle-based liquid simulation. The proposed network
leverages neighborhood contributions to encode inherent liquid properties
throughout convolutions. We also propose a particle-based approach to interpolate between liquids generated from varying simulation discretizations using a state-of-the-art bidirectional optical flow solver method for fluids in addition with a novel key-event topological alignment constraint. In conjunction with the neighborhood contributions, our loss formulation allows the inference model throughout epochs to reward important differences in regard to significant gaps in simulation discretizations. Even when applied in an untested simulation setup, our approach is able to generate plausible high-resolution details. Using this interpolation approach and the predicted displacements, our approach combines the input liquid properties with the predicted motion to infer semi-Lagrangian advection. We furthermore show-case how the proposed interpolation approach can facilitate generating large simulation datasets with a subset of initial condition parameters.

Neural UpFlow: A Scene Flow Learning Approach to Increase the Apparent Resolution of Particle-Based Liquids